The former England midfielder was appointed as Andre Villas-Boas' successor in December after the Portuguese left White Hart Lane by mutual consent.
Sherwood has guided the London club to fifth in the Premier League and ensured they progressed to the last 16 of the UEFA Europa League.
The 45-year-old, who played 93 times for Tottenham during his playing days, was only given the role until the end of the season, though, and his future is uncertain.
Ronald de Boer this week claimed his brother Frank, the Ajax coach, was approached to take over at White Hart Lane before Sherwood was handed the reins.
Sherwood is in the dark as to whether he will stay on in his role, but is confident that given time he can bring success to the club.
"That (public backing) is up to the club," Sherwood said. "They are obviously going to keep their options open and decide what they want to do in the future.
"It is something I can't comment on and I wouldn't. If the club feel they want to come out and back me, then it is up to them. If they don't, I am just cracking on. I am not going to be a different person for it.
"I honestly believe I can be a good manager in time. That said, I keep saying time but I am realistic enough to know that you don't get given time."
When asked if he feels he has been given credit for the job he has done so far, Sherwood said: "No, probably not. People have been waiting for us to fail and lose some games. I don't know why. I just think the perception is you cannot be a rookie manager and come in and be that good.
"I speak to a lot of managers and I say 'Are you living on game to game?' Sometimes it's not but at a club like Tottenham it absolutely is.
"If we lose away at Norwich it is a 'disaster' and I am one game away from complete catastrophic disaster. So I just have to get on with it. I know that. There is a lot of pressure but I didn't expect any different."
Tottenham make the short trip London rivals Chelsea at Stamford Bridge on Saturday looking for their first win at Stamford Bridge for just over 24 years.
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